%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV401^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:50:02 AM UTC 2026
% Result : Theorem 0.09s 0.27s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 1
% Syntax : Number of formulae : 86 ( 53 unt; 0 typ; 0 def)
% Number of atoms : 485 ( 124 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 725 ( 80 ~; 100 |; 6 &; 496 @)
% ( 4 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 118 ( 118 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 218 ( 0 ^; 218 !; 0 ?; 218 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_cF,type,
cF: ( a > $o ) > a > $o ).
thf(tp_cG,type,
cG: ( a > $o ) > a > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: a > $o ).
thf(tp_sK2_SY17,type,
sK2_SY17: a ).
thf(tp_sK3_SY15,type,
sK3_SY15: ( a > $o ) > ( a > $o ) > a ).
thf(tp_sK4_SX0,type,
sK4_SX0: a > $o ).
thf(tp_sK5_SY25,type,
sK5_SY25: a ).
thf(tp_sK6_SY23,type,
sK6_SY23: ( a > $o ) > ( a > $o ) > a ).
thf(1,conjecture,
( ( ! [S: a > $o,T: a > $o] :
( ! [Xx: a] :
( ( S @ Xx )
=> ( T @ Xx ) )
=> ! [Xx: a] :
( ( cF @ T @ Xx )
=> ( cF @ S @ Xx ) ) )
& ! [S: a > $o,Xx: a] :
( ( S @ Xx )
=> ( cF @ ( cG @ S ) @ Xx ) )
& ! [S: a > $o,Xx: a] :
( ( S @ Xx )
=> ( cG @ ( cF @ S ) @ Xx ) ) )
=> ! [S: a > $o,Xx: a] :
( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
<=> ( cF @ S @ Xx ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM67_pme) ).
thf(2,negated_conjecture,
( ( ( ! [S: a > $o,T: a > $o] :
( ! [Xx: a] :
( ( S @ Xx )
=> ( T @ Xx ) )
=> ! [Xx: a] :
( ( cF @ T @ Xx )
=> ( cF @ S @ Xx ) ) )
& ! [S: a > $o,Xx: a] :
( ( S @ Xx )
=> ( cF @ ( cG @ S ) @ Xx ) )
& ! [S: a > $o,Xx: a] :
( ( S @ Xx )
=> ( cG @ ( cF @ S ) @ Xx ) ) )
=> ! [S: a > $o,Xx: a] :
( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
<=> ( cF @ S @ Xx ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [S: a > $o,T: a > $o] :
( ! [Xx: a] :
( ( S @ Xx )
=> ( T @ Xx ) )
=> ! [Xx: a] :
( ( cF @ T @ Xx )
=> ( cF @ S @ Xx ) ) )
& ! [S: a > $o,Xx: a] :
( ( S @ Xx )
=> ( cF @ ( cG @ S ) @ Xx ) )
& ! [S: a > $o,Xx: a] :
( ( S @ Xx )
=> ( cG @ ( cF @ S ) @ Xx ) ) )
=> ! [S: a > $o,Xx: a] :
( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
<=> ( cF @ S @ Xx ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [S: a > $o,T: a > $o] :
( ! [Xx: a] :
( ( S @ Xx )
=> ( T @ Xx ) )
=> ! [Xx: a] :
( ( cF @ T @ Xx )
=> ( cF @ S @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [S: a > $o,Xx: a] :
( ( S @ Xx )
=> ( cF @ ( cG @ S ) @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [S: a > $o,Xx: a] :
( ( S @ Xx )
=> ( cG @ ( cF @ S ) @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [S: a > $o,Xx: a] :
( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
<=> ( cF @ S @ Xx ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [S: a > $o,Xx: a] :
( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
=> ( cF @ S @ Xx ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[7]) ).
thf(9,plain,
( ( ! [S: a > $o,Xx: a] :
( ( cF @ S @ Xx )
=> ( cF @ ( cG @ ( cF @ S ) ) @ Xx ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[7]) ).
thf(10,plain,
( ( ~ ! [S: a > $o,Xx: a] :
( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
=> ( cF @ S @ Xx ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ! [S: a > $o,Xx: a] :
( ( cF @ S @ Xx )
=> ( cF @ ( cG @ ( cF @ S ) ) @ Xx ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(12,plain,
( ( ! [S: a > $o,Xx: a] :
( ( S @ Xx )
=> ( cG @ ( cF @ S ) @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(13,plain,
( ( ! [S: a > $o,Xx: a] :
( ( S @ Xx )
=> ( cF @ ( cG @ S ) @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(14,plain,
( ( ! [S: a > $o,T: a > $o] :
( ! [Xx: a] :
( ( S @ Xx )
=> ( T @ Xx ) )
=> ! [Xx: a] :
( ( cF @ T @ Xx )
=> ( cF @ S @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(15,plain,
( ( ~ ! [S: a > $o,Xx: a] :
( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
=> ( cF @ S @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(16,plain,
( ( ! [SX0: a > $o,SX1: a > $o] :
( ~ ! [SX2: a] :
( ~ ( SX0 @ SX2 )
| ( SX1 @ SX2 ) )
| ! [SX2: a] :
( ~ ( cF @ SX1 @ SX2 )
| ( cF @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(17,plain,
( ( ! [SX0: a > $o,SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cF @ ( cG @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(18,plain,
( ( ! [SX0: a > $o,SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cG @ ( cF @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(19,plain,
( ( ~ ! [SX0: a > $o,SX1: a] :
( ~ ( cF @ ( cG @ ( cF @ SX0 ) ) @ SX1 )
| ( cF @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(20,plain,
! [SV1: a > $o] :
( ( ! [SY10: a > $o] :
( ~ ! [SY11: a] :
( ~ ( SV1 @ SY11 )
| ( SY10 @ SY11 ) )
| ! [SY12: a] :
( ~ ( cF @ SY10 @ SY12 )
| ( cF @ SV1 @ SY12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(21,plain,
! [SV2: a > $o] :
( ( ! [SY13: a] :
( ~ ( SV2 @ SY13 )
| ( cF @ ( cG @ SV2 ) @ SY13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(22,plain,
! [SV3: a > $o] :
( ( ! [SY14: a] :
( ~ ( SV3 @ SY14 )
| ( cG @ ( cF @ SV3 ) @ SY14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
( ( ! [SX0: a > $o,SX1: a] :
( ~ ( cF @ ( cG @ ( cF @ SX0 ) ) @ SX1 )
| ( cF @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(24,plain,
! [SV4: a > $o,SV1: a > $o] :
( ( ~ ! [SY15: a] :
( ~ ( SV1 @ SY15 )
| ( SV4 @ SY15 ) )
| ! [SY16: a] :
( ~ ( cF @ SV4 @ SY16 )
| ( cF @ SV1 @ SY16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(25,plain,
! [SV5: a,SV2: a > $o] :
( ( ~ ( SV2 @ SV5 )
| ( cF @ ( cG @ SV2 ) @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV6: a,SV3: a > $o] :
( ( ~ ( SV3 @ SV6 )
| ( cG @ ( cF @ SV3 ) @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(27,plain,
( ( ! [SY17: a] :
( ~ ( cF @ ( cG @ ( cF @ sK1_SX0 ) ) @ SY17 )
| ( cF @ sK1_SX0 @ SY17 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[23]) ).
thf(28,plain,
! [SV4: a > $o,SV1: a > $o] :
( ( ( ~ ! [SY15: a] :
( ~ ( SV1 @ SY15 )
| ( SV4 @ SY15 ) ) )
= $true )
| ( ( ! [SY16: a] :
( ~ ( cF @ SV4 @ SY16 )
| ( cF @ SV1 @ SY16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(29,plain,
! [SV5: a,SV2: a > $o] :
( ( ( ~ ( SV2 @ SV5 ) )
= $true )
| ( ( cF @ ( cG @ SV2 ) @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(30,plain,
! [SV6: a,SV3: a > $o] :
( ( ( ~ ( SV3 @ SV6 ) )
= $true )
| ( ( cG @ ( cF @ SV3 ) @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(31,plain,
( ( ~ ( cF @ ( cG @ ( cF @ sK1_SX0 ) ) @ sK2_SY17 )
| ( cF @ sK1_SX0 @ sK2_SY17 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[27]) ).
thf(32,plain,
! [SV4: a > $o,SV1: a > $o] :
( ( ( ! [SY15: a] :
( ~ ( SV1 @ SY15 )
| ( SV4 @ SY15 ) ) )
= $false )
| ( ( ! [SY16: a] :
( ~ ( cF @ SV4 @ SY16 )
| ( cF @ SV1 @ SY16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV5: a,SV2: a > $o] :
( ( ( SV2 @ SV5 )
= $false )
| ( ( cF @ ( cG @ SV2 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV6: a,SV3: a > $o] :
( ( ( SV3 @ SV6 )
= $false )
| ( ( cG @ ( cF @ SV3 ) @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(35,plain,
( ( ~ ( cF @ ( cG @ ( cF @ sK1_SX0 ) ) @ sK2_SY17 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(36,plain,
( ( cF @ sK1_SX0 @ sK2_SY17 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(37,plain,
! [SV4: a > $o,SV1: a > $o] :
( ( ( ~ ( SV1 @ ( sK3_SY15 @ SV4 @ SV1 ) )
| ( SV4 @ ( sK3_SY15 @ SV4 @ SV1 ) ) )
= $false )
| ( ( ! [SY16: a] :
( ~ ( cF @ SV4 @ SY16 )
| ( cF @ SV1 @ SY16 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[32]) ).
thf(38,plain,
( ( cF @ ( cG @ ( cF @ sK1_SX0 ) ) @ sK2_SY17 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(39,plain,
! [SV4: a > $o,SV1: a > $o] :
( ( ( ~ ( SV1 @ ( sK3_SY15 @ SV4 @ SV1 ) ) )
= $false )
| ( ( ! [SY16: a] :
( ~ ( cF @ SV4 @ SY16 )
| ( cF @ SV1 @ SY16 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(40,plain,
! [SV1: a > $o,SV4: a > $o] :
( ( ( SV4 @ ( sK3_SY15 @ SV4 @ SV1 ) )
= $false )
| ( ( ! [SY16: a] :
( ~ ( cF @ SV4 @ SY16 )
| ( cF @ SV1 @ SY16 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(41,plain,
! [SV4: a > $o,SV1: a > $o] :
( ( ( SV1 @ ( sK3_SY15 @ SV4 @ SV1 ) )
= $true )
| ( ( ! [SY16: a] :
( ~ ( cF @ SV4 @ SY16 )
| ( cF @ SV1 @ SY16 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(42,plain,
! [SV1: a > $o,SV7: a,SV4: a > $o] :
( ( ( ~ ( cF @ SV4 @ SV7 )
| ( cF @ SV1 @ SV7 ) )
= $true )
| ( ( SV4 @ ( sK3_SY15 @ SV4 @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(43,plain,
! [SV1: a > $o,SV8: a,SV4: a > $o] :
( ( ( ~ ( cF @ SV4 @ SV8 )
| ( cF @ SV1 @ SV8 ) )
= $true )
| ( ( SV1 @ ( sK3_SY15 @ SV4 @ SV1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(44,plain,
! [SV1: a > $o,SV7: a,SV4: a > $o] :
( ( ( ~ ( cF @ SV4 @ SV7 ) )
= $true )
| ( ( cF @ SV1 @ SV7 )
= $true )
| ( ( SV4 @ ( sK3_SY15 @ SV4 @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(45,plain,
! [SV1: a > $o,SV8: a,SV4: a > $o] :
( ( ( ~ ( cF @ SV4 @ SV8 ) )
= $true )
| ( ( cF @ SV1 @ SV8 )
= $true )
| ( ( SV1 @ ( sK3_SY15 @ SV4 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(46,plain,
! [SV1: a > $o,SV7: a,SV4: a > $o] :
( ( ( cF @ SV4 @ SV7 )
= $false )
| ( ( cF @ SV1 @ SV7 )
= $true )
| ( ( SV4 @ ( sK3_SY15 @ SV4 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(47,plain,
! [SV1: a > $o,SV8: a,SV4: a > $o] :
( ( ( cF @ SV4 @ SV8 )
= $false )
| ( ( cF @ SV1 @ SV8 )
= $true )
| ( ( SV1 @ ( sK3_SY15 @ SV4 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(48,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[33,47,46,38,36,34]) ).
thf(49,plain,
( ( ! [S: a > $o,Xx: a] :
( ( S @ Xx )
=> ( cG @ ( cF @ S ) @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(50,plain,
( ( ! [S: a > $o,Xx: a] :
( ( S @ Xx )
=> ( cF @ ( cG @ S ) @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(51,plain,
( ( ! [S: a > $o,T: a > $o] :
( ! [Xx: a] :
( ( S @ Xx )
=> ( T @ Xx ) )
=> ! [Xx: a] :
( ( cF @ T @ Xx )
=> ( cF @ S @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(52,plain,
( ( ~ ! [S: a > $o,Xx: a] :
( ( cF @ S @ Xx )
=> ( cF @ ( cG @ ( cF @ S ) ) @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(53,plain,
( ( ! [SX0: a > $o,SX1: a > $o] :
( ~ ! [SX2: a] :
( ~ ( SX0 @ SX2 )
| ( SX1 @ SX2 ) )
| ! [SX2: a] :
( ~ ( cF @ SX1 @ SX2 )
| ( cF @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(54,plain,
( ( ! [SX0: a > $o,SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cG @ ( cF @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(55,plain,
( ( ~ ! [SX0: a > $o,SX1: a] :
( ~ ( cF @ SX0 @ SX1 )
| ( cF @ ( cG @ ( cF @ SX0 ) ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(56,plain,
( ( ! [SX0: a > $o,SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cF @ ( cG @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(57,plain,
! [SV9: a > $o] :
( ( ! [SY18: a > $o] :
( ~ ! [SY19: a] :
( ~ ( SV9 @ SY19 )
| ( SY18 @ SY19 ) )
| ! [SY20: a] :
( ~ ( cF @ SY18 @ SY20 )
| ( cF @ SV9 @ SY20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(58,plain,
! [SV10: a > $o] :
( ( ! [SY21: a] :
( ~ ( SV10 @ SY21 )
| ( cG @ ( cF @ SV10 ) @ SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(59,plain,
( ( ! [SX0: a > $o,SX1: a] :
( ~ ( cF @ SX0 @ SX1 )
| ( cF @ ( cG @ ( cF @ SX0 ) ) @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(60,plain,
! [SV11: a > $o] :
( ( ! [SY22: a] :
( ~ ( SV11 @ SY22 )
| ( cF @ ( cG @ SV11 ) @ SY22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(61,plain,
! [SV12: a > $o,SV9: a > $o] :
( ( ~ ! [SY23: a] :
( ~ ( SV9 @ SY23 )
| ( SV12 @ SY23 ) )
| ! [SY24: a] :
( ~ ( cF @ SV12 @ SY24 )
| ( cF @ SV9 @ SY24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(62,plain,
! [SV13: a,SV10: a > $o] :
( ( ~ ( SV10 @ SV13 )
| ( cG @ ( cF @ SV10 ) @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(63,plain,
( ( ! [SY25: a] :
( ~ ( cF @ sK4_SX0 @ SY25 )
| ( cF @ ( cG @ ( cF @ sK4_SX0 ) ) @ SY25 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[59]) ).
thf(64,plain,
! [SV14: a,SV11: a > $o] :
( ( ~ ( SV11 @ SV14 )
| ( cF @ ( cG @ SV11 ) @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(65,plain,
! [SV12: a > $o,SV9: a > $o] :
( ( ( ~ ! [SY23: a] :
( ~ ( SV9 @ SY23 )
| ( SV12 @ SY23 ) ) )
= $true )
| ( ( ! [SY24: a] :
( ~ ( cF @ SV12 @ SY24 )
| ( cF @ SV9 @ SY24 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(66,plain,
! [SV13: a,SV10: a > $o] :
( ( ( ~ ( SV10 @ SV13 ) )
= $true )
| ( ( cG @ ( cF @ SV10 ) @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(67,plain,
( ( ~ ( cF @ sK4_SX0 @ sK5_SY25 )
| ( cF @ ( cG @ ( cF @ sK4_SX0 ) ) @ sK5_SY25 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[63]) ).
thf(68,plain,
! [SV14: a,SV11: a > $o] :
( ( ( ~ ( SV11 @ SV14 ) )
= $true )
| ( ( cF @ ( cG @ SV11 ) @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(69,plain,
! [SV12: a > $o,SV9: a > $o] :
( ( ( ! [SY23: a] :
( ~ ( SV9 @ SY23 )
| ( SV12 @ SY23 ) ) )
= $false )
| ( ( ! [SY24: a] :
( ~ ( cF @ SV12 @ SY24 )
| ( cF @ SV9 @ SY24 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(70,plain,
! [SV13: a,SV10: a > $o] :
( ( ( SV10 @ SV13 )
= $false )
| ( ( cG @ ( cF @ SV10 ) @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(71,plain,
( ( ~ ( cF @ sK4_SX0 @ sK5_SY25 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(72,plain,
( ( cF @ ( cG @ ( cF @ sK4_SX0 ) ) @ sK5_SY25 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(73,plain,
! [SV14: a,SV11: a > $o] :
( ( ( SV11 @ SV14 )
= $false )
| ( ( cF @ ( cG @ SV11 ) @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(74,plain,
! [SV12: a > $o,SV9: a > $o] :
( ( ( ~ ( SV9 @ ( sK6_SY23 @ SV12 @ SV9 ) )
| ( SV12 @ ( sK6_SY23 @ SV12 @ SV9 ) ) )
= $false )
| ( ( ! [SY24: a] :
( ~ ( cF @ SV12 @ SY24 )
| ( cF @ SV9 @ SY24 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[69]) ).
thf(75,plain,
( ( cF @ sK4_SX0 @ sK5_SY25 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(76,plain,
! [SV12: a > $o,SV9: a > $o] :
( ( ( ~ ( SV9 @ ( sK6_SY23 @ SV12 @ SV9 ) ) )
= $false )
| ( ( ! [SY24: a] :
( ~ ( cF @ SV12 @ SY24 )
| ( cF @ SV9 @ SY24 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(77,plain,
! [SV9: a > $o,SV12: a > $o] :
( ( ( SV12 @ ( sK6_SY23 @ SV12 @ SV9 ) )
= $false )
| ( ( ! [SY24: a] :
( ~ ( cF @ SV12 @ SY24 )
| ( cF @ SV9 @ SY24 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(78,plain,
! [SV12: a > $o,SV9: a > $o] :
( ( ( SV9 @ ( sK6_SY23 @ SV12 @ SV9 ) )
= $true )
| ( ( ! [SY24: a] :
( ~ ( cF @ SV12 @ SY24 )
| ( cF @ SV9 @ SY24 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(79,plain,
! [SV9: a > $o,SV15: a,SV12: a > $o] :
( ( ( ~ ( cF @ SV12 @ SV15 )
| ( cF @ SV9 @ SV15 ) )
= $true )
| ( ( SV12 @ ( sK6_SY23 @ SV12 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(80,plain,
! [SV9: a > $o,SV16: a,SV12: a > $o] :
( ( ( ~ ( cF @ SV12 @ SV16 )
| ( cF @ SV9 @ SV16 ) )
= $true )
| ( ( SV9 @ ( sK6_SY23 @ SV12 @ SV9 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(81,plain,
! [SV9: a > $o,SV15: a,SV12: a > $o] :
( ( ( ~ ( cF @ SV12 @ SV15 ) )
= $true )
| ( ( cF @ SV9 @ SV15 )
= $true )
| ( ( SV12 @ ( sK6_SY23 @ SV12 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(82,plain,
! [SV9: a > $o,SV16: a,SV12: a > $o] :
( ( ( ~ ( cF @ SV12 @ SV16 ) )
= $true )
| ( ( cF @ SV9 @ SV16 )
= $true )
| ( ( SV9 @ ( sK6_SY23 @ SV12 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(83,plain,
! [SV9: a > $o,SV15: a,SV12: a > $o] :
( ( ( cF @ SV12 @ SV15 )
= $false )
| ( ( cF @ SV9 @ SV15 )
= $true )
| ( ( SV12 @ ( sK6_SY23 @ SV12 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(84,plain,
! [SV9: a > $o,SV16: a,SV12: a > $o] :
( ( ( cF @ SV12 @ SV16 )
= $false )
| ( ( cF @ SV9 @ SV16 )
= $true )
| ( ( SV9 @ ( sK6_SY23 @ SV12 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(85,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[70,84,83,75,73,72]) ).
thf(86,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[85,48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV401^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.20 % Computer : n020.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Oct 6 15:47:06 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.27
% 0.09/0.27 No.of.Axioms: 0
% 0.09/0.27
% 0.09/0.27 Length.of.Defs: 0
% 0.09/0.27
% 0.09/0.27 Contains.Choice.Funs: false
% 0.09/0.27 ..
% 0.09/0.27
% 0.09/0.27 ********************************
% 0.09/0.27 * All subproblems solved! *
% 0.09/0.27 ********************************
% 0.09/0.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:85,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.27
% 0.09/0.27 %**** Beginning of derivation protocol ****
% 0.09/0.27 % SZS output start CNFRefutation
% See solution above
% 0.09/0.28
% 0.09/0.28 %**** End of derivation protocol ****
% 0.09/0.28 %**** no. of clauses in derivation: 86 ****
% 0.09/0.28 %**** clause counter: 85 ****
% 0.09/0.28
% 0.09/0.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:85,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------